you can do some custom in activity method: onActionModeStarted(ActionMode mode),
just like this:
@Override
public void onActionModeStarted(ActionMode mode) {
    if (mActionMode == null) {
        mActionMode = mode;
        Menu menu = mode.getMenu();
        menu.clear();
        getMenuInflater().inflate(R.menu.YOUR_MENU, menu);
        List<MenuItem> menuItems = new ArrayList<>();
        // get custom menu item
        for (int i = 0; i < menu.size(); i++) {
            menuItems.add(menu.getItem(i));
        }
        menu.clear();
        // reset menu item order
        int size = menuItems.size();
        for (int i = 0; i < size; i++) {
            addMenuItem(menu, menuItems.get(i), i, true);
        }
        super.onActionModeStarted(mode);
    }
}
/**
 * add custom item to menu
 * @param menu
 * @param item
 * @param order
 * @param isClick
 */
private void addMenuItem(Menu menu, MenuItem item, int order, boolean isClick){
    MenuItem menuItem = menu.add(item.getGroupId(),
            item.getItemId(),
            order,
            item.getTitle());
    menuItem.setShowAsAction(MenuItem.SHOW_AS_ACTION_ALWAYS);
    if (isClick)
        // set custom menu item click
        menuItem.setOnMenuItemClickListener(this);
}